A175373 Partial sums of A175372.

1, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 13, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25

Offset

0,2

Comments

Number of integer pairs (x,y) satisfying x^4+y^4 <= n, any -n <= x,y <=n.

Links

Table of n, a(n) for n=0..74.

Example

a(6) = 9 counts (x,y) = (-1,-1), (-1,0), (-1,1), (0,-1), (0,0), (0,1), (1,-1), (1,0) and (1,1).

Prog

(Python)
from math import isqrt
def A175373(n): return 1+(sum(isqrt(isqrt(n-x**4)) for x in range(isqrt(isqrt(n))+1))<<2) # Chai Wah Wu, Feb 23 2026

Crossrefs

Cf. A057655, A175363.

Sequence in context: A020846 A180014 A105643 * A175363 A073168 A315121

Adjacent sequences: A175370 A175371 A175372 * A175374 A175375 A175376

Keyword

nonn

Author

R. J. Mathar, Apr 24 2010

Status

approved